Coverage fraction, bubble

Electrochemical discharges have all the characteristics of arc discharges. They occur in a very similar voltage range with similar currents and at atmospheric pressure. The question remains as to how these arcs can be initiated. We have proposed the hypothesis that the ignition is thermal [123]. The cathode temperature required is probably reached before the gas film is totally formed,3 when the active electrode bubble coverage fraction reaches its maximum value. 

Note that, in this description, the shadowing of the surface by the bubbles in the adherence region was not considered. With increasing bubble coverage fraction 6, the resistance in the diffusion region ff will also increase. A possible ansatz is to write (3.44) as ... 

The evolution of bubbles on a gas evolving electrode is a dynamic process. As described in previous sections, percolation theory can help to quantify the bubble size distribution in the adherence region if the mean bubble coverage fraction 9 is known. In order to derive an equation describing the evolution of 6 for gas evolving electrodes, we will write a mass balance equation between the amount of gas produced and the quantity of gas leaving the adherence region [125,129]. Faraday s law computes VG, the amount of gas produced per unit time at an electrode ... 

The evolution equation of the bubble coverage fraction 9 is as follows ... 

The stationary mean bubble coverage fraction 0s is given by the stationary solution of Equation (3.61) ... 

To evaluate the sum from Equation (3.68), we will use the approximation smax = oo in the following paragraphs. As long as 9 is smaller than the percolation threshold pc, the stationary bubble coverage fraction is given by ... 

In a similar manner, one can write a relation between the terminal voltage and the stationary bubble coverage fraction (9s < pc) ... 

Increase in the nominal current density With increasing nominal current density I/A, the bubble coverage fraction increases. When it reaches a critical value, as computed by (4.16), a gas film is formed. Such a scenario happens, for example, in current-controlled cells or, as will be seen in Section 4.1.3, in a voltage-controlled cell if for some reason the inter-electrode resistance decreases. 

Figure 4.7 Step input for a terminal voltage lower than the critical voltage (a) bubble coverage fraction 0 step input (b) normalised current J step input.

For higher terminal voltages, the bubble coverage fraction will grow according to Equation (4.22) until it reaches the percolation threshold where the gas film forms. The time tf until pc is attained is given by the solution of 0 t f) — Pc One obtains for the gas film formation time (Fig. 4.8) ... 

In equation 5, C is amorphous carbon and CF2 changes to many perfluorocarbons, such as CF4, C2F6, etc., by secondary reactions. The surface coverage of graphite fluoride on the anode depends on the relative reaction rates of equations 4 and 5. Equation 6 has been introduced to analyze the wettability of the carbon surface with graphite fluoride formed on it.2 It shows the relationship between the fraction of effective surface for equation 3 per unit surface area of carbon (a) and the contact angle (0) of a fluorine gas bubble on the surface of the carbon electrode.2... 

Fig. 13.33 Fractional coverage predicted by simulations (solid circles) in comparison with the experiments of Taylor (62) (open diamond) and Hyzyak and Koelling (67). [Reprinted by permission from V. Gauri and K. W. Koelling, Gas-assisted Displacement of Viscoelastic Fluids Flow Dynamics at the Bubble Front, J. Non-Newt. Fluid Meek, 83, 183-203 (1999).]...

In the case of incomplete coverage by the bubbles, they only occupy a small fraction of the surface. We can calculate [85,86] the molar volume of the gas, V, in this case using the critical value of a spherical bubble ... 

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